Method for constructing quadrants with multiple independent biomarkers for diagnosing diseases

ABSTRACT

The present invention relates to a method for constructing quadrants corresponding to different diseases in a frame of concentrations of multiple independent biomarkers, comprising:
         (a) transferring original distributed concentrations of every independent biomarker to modified distributed concentrations, comprising:
           calculating the mean value and the standard deviation of the original distributed concentrations for a given independent biomarker;   individually subtracting all the original distributed concentrations by the mean value for the given independent biomarker; and   individually dividing all the differences by the standard deviation to get the modified distributed concentrations for the given independent biomarker;   
           (b) positing the modified distributed concentrations in a frame of multiple independent biomarkers; and   (c) finding a boundary optimally separating neighboring quadrants corresponding to different diseases.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationNo. 62/188,629 filed on Jul. 4, 2015, incorporated herein by referencein its entirety.

FIELD OF THE INVENTION

The present invention relates to a method for constructing quadrantswith multiple independent biomarkers for diagnosing diseases.

BACKGROUND OF THE INVENTION

Neurodegenerative diseases include several kinds of pathologies causingversatile diseases, such as Alzheimer's disease (AD), Parkinson'sdisease (PD), dementia with Lewy body (DLB), and frontotemporal dementia(FTD), etc. Due to different causes, these diseases may develop variousimpaired clearance of biomolecules, which are regarded as biomarkerswith these diseases. For example, β-amyloid (Aβ), tau protein and theirderivates are typically related to AD, while α-synuclein and itsderivates are representative biomarkers for PD and DLB. It is suggestedto discriminate patients by assaying the typical biomarkers. Forexample, AD patients show higher values for the product inconcentrations of plasma Aβ₁₋₄₂ and tau protein, denoted asφ_(Aβ1-42)×φ_(tau), as compared to that of normal controls (NC, orreferred as to healthy subjects) and DLB patients, as shown in FIG. 1A.But, in FIG. 1A, DLB patients will be miss-diagnosed as normal controls.As the plasma α-synuclein is assayed for NC, DLB patients, and ADpatients, patients with DLB show higher concentrations of plasmaα-synuclein, denoted as φ_(α-syn), as compared to NC, as shown in FIG.1B. However, some AD patients also show the same levels of plasmaα-synuclein as DLB patients. Thus, DLB patients can not be welldiscriminated from AD patients by merely assaying φ_(α-syn). Accordingto results in FIGS. 1A and 1B, DLB patients can not be accuratelydiagnosed by assaying either of plasma φ_(Aβ1-42)×φ_(tau) or plasmaφ_(α-syn).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A: Detected concentration products of plasma Aβ₁₋₄₂ and tauprotein for normal controls (NC) and patients with either dementia withLewy Body (DLB) or Alzheimer's disease (AD). FIG. 1B: Detectedconcentrations of plasma α-synuclein for normal controls (NC) andpatients with either dementia with Lewy Body (DLB) or Alzheimer'sdisease (AD).

FIG. 2: A proposed flow chart to discriminate subjects belonging to NC,AD, or DLB group by assaying multiple bio-markers.

FIG. 3A: Detected concentrations of Aβ₁₋₄₂ in plasma with variouslyneurodegenerative diseases. FIG. 3B: Detected concentrations of tauprotein in plasma with variously neurodegenerative diseases. FIG. 3C:Detected concentrations of α-synuclein in plasma with variouslyneurodegenerative diseases.

FIG. 4: Product in concentrations of plasma Aβ₁₋₄₂ and tau protein forall subjects.

FIG. 5: A proposed flow chart to discriminate subjects in variousdisease groups by assaying multiple bio-markers.

FIG. 6: Detected values in the frame of plasma φ_(Aβ1-42)×φ_(tau) andplasma φ_(α-syn) for all subjects.

FIG. 7: Illustration of the polar angle θ to discriminate disease groupsin the frame of plasma φ_(Aβ1-42)×φ_(tau) and plasma φ_(α-syn) for allsubjects.

FIG. 8: Distribution of original concentrations, log(φ_(α-syn)) andlog(φ_(Aβ1-42)×φ_(tau)) for variously disease groups.

FIG. 9: Distribution of modulated concentrations in the frame ofφ′_(α-syn) and φ′_(Aβ1-42)×φ_(tau) for variously disease groups.

FIG. 10: Shifted polar angles θ′_(s) for NC group and DLB group in FIG.9.

FIG. 11: Boundary guided with the ray along the polar angle 189.48°optimally discriminating NC and DLB subjects.

FIG. 12: Boundaries denoted with rays along specific polar angles tooptimally discriminating subjects with NC (•), DLB (♦), PD (▴), AD (+),or FTD (▪).

SUMMARY OF THE INVENTION

The present invention relates to a method for constructing quadrantscorresponding to different diseases in a frame of concentrations ofmultiple independent biomarkers, comprising:

-   -   (a) transferring original distributed concentrations of every        independent biomarker to modified distributed concentrations,        comprising:        -   calculating the mean value and the standard deviation of the            original distributed concentrations for a given independent            biomarker;        -   individually subtracting all the original distributed            concentrations by the mean value for the given independent            biomarker; and        -   individually dividing all the differences by the standard            deviation to get the modified distributed concentrations for            the given independent biomarker;    -   (b) positing the modified distributed concentrations in a frame        of multiple independent biomarkers; and    -   (c) finding a boundary optimally separating neighboring        quadrants corresponding to different diseases.

DETAILED DESCRIPTION OF THE INVENTION

It is proposed that DLB patients can be discriminated from NC and AD, asillustrated in FIG. 2. By firstly assaying plasma α-synuclein and thenassaying plasma Aβ₁₋₄₂ and tau protein, DLB patients show higherφ_(α-syn) and lower φ_(Aβ1-42)×φ_(tau), AD patients show higherφ_(Aβ1-42)×φ_(tau), and NC subjects show lower φ_(α-syn) and lowerφ_(Aβ1-42)×φ_(tau). The illustration in FIG. 2 reveals the possibilityto achieve high clinical sensitivity and specificity in discriminatingpatients with DLB or other neurodegenerative diseases such as AD, PD,and FTD by assaying multiple biomarkers.

Therefore, the present invention is to investigate a method fordiscriminating patients with different diseases by assaying multiplebiomarkers.

The present invention provides a method for constructing quadrantscorresponding to different diseases in a frame of concentrations ofmultiple independent biomarkers, comprising:

-   -   (a) transferring original distributed concentrations of every        independent biomarker to modified distributed concentrations,        comprising:        -   calculating the mean value and the standard deviation of the            original distributed concentrations for a given independent            biomarker;        -   individually subtracting all the original distributed            concentrations by the mean value for the given independent            biomarker; and        -   individually dividing all the differences by the standard            deviation to get the modified distributed concentrations for            the given independent biomarker;    -   (b) positing the modified distributed concentrations in a frame        of multiple independent biomarkers; and    -   (c) finding a boundary optimally separating neighboring        quadrants corresponding to different diseases.

In an embodiment, the original distributed concentrations are eitheroriginally detected concentrations or transferred concentrations of theoriginally detected concentrations via mathematic calculation. Themathematic calculation may be, but not limited to, logarithm,trigonometric function, sigmoid function, or any combinations thereof.

In an embodiment, the independent biomarker may be either a single kindof bio-molecule or a combination of several kinds of bio-molecules. Theindependent biomarker may exist in, but not limited to, blood, urine,cerebrospinal fluid, or saliva.

In an embodiment, the number of the multiple independent biomarkers ismore than one.

In an embodiment, the method for finding a boundary optimally separatingneighboring quadrants corresponding to different diseases in step (c) isROC curve analysis.

In an embodiment, the independent biomarkers may be, but not limited to,plasma α-synuclein, β-amyloid, tau protein, and their derivatives toconstruct quadrants corresponding to healthy subjects and patients withneurodegenerative disease. The neurodegenerative disease may be, but notlimited to, dementia with Lewy body, Parkinson's disease, Alzheimer'sdisease, or frontotemporal dementia.

EXAMPLES

The examples below are non-limiting and are merely representative ofvarious aspects and features of the present invention. Therefore, themethod of the present invention should not be limited to only fordiagnosing neurodegenerative disease.

Example 1 Subjects

Subjects including normal controls (n=6), DLB patients (n=9), ADpatients (n=6), PD patients (n=9), and FTD patients (n=6) were enrolled.The ages of all subjects were from 47 to 87 years. The demographicinformation of subjects was listed in Table 1. The subjects were dividedinto disease groups according to neuropsychological tests and clinicalsymptoms. Some subjects were examined with magnetic resonance imaging.There was no combination of these diseases for any one of subjects. Theplasma biomarkers Aβ₁₋₄₂, tau protein, and α-synuclein were assayed foreach subject by using immunomagnetic reduction (Yang, C. C., Yang, S.Y., Chieh, J. J., Horng, H. E., Hong, C. Y., Yang, H. C., Chen, K. H.,Shih, B. Y., Chen, T. F., Chiu, M. J. (2011) Biofunctionalized magneticnanoparticles for specifically detecting biomarkers of Alzheimer'sdisease in vitro. ACS Chem. Neurosci. 2, 500-505; Chiu, M. J., Yang, S.Y., Chen, T. F., Chieh, J. J., Huang, T. Z., Yip, P. K., Yang, H. C.,Cheng, T. W., Chen, Y. F., Hua, M. S., and Horng, H. E. (2012) New assayfor old markers-plasma beta amyloid of mild cognitive impairment andAlzheimer's disease. Curr. Alzheimer Res. 9, 1142-1147; Yang, S. Y.,Chieh, J. J., Yang, C. C., Liao, S. H., Chen, H. H., Horng, H. E., Yang,H. C., Hong, C. Y., Chiu, M. J., Chen, T. F., Huang, K. W., and Wu, C.C. (2013) Clinic applications in assaying ultra-low-concentrationbio-markers using HTS SQUID-based AC magnetosusceptometer. IEEE Trans.Appl. Supercond. 23, 1600604-1600607; Chiu, M. J., Chen, Y. F., Chen, T.F., Yang, S. Y., Yang, F. P. Gloria, Tseng, T. W., Chieh, J. J., Chen,J. C. Rare, Tzen, K. Y., Hua, M. S., and Horng, H. E. (2013) Plasma tauas a window to the brain-negative associations with brain volume andmemory function in mild cognitive impairment and early alzheimer'sdisease. Human Barin Mapping, 35, 3132-3142; Tzen, K. Y., Yang, S. Y.,Chen, T. F., Cheng, T. W., Horng, H. E., Wen, H. P., Huang, Y. Y.,Shiue, C. Y., and Chiu, M. J. (2014) Plasma Aβ but not tau related tobrain PiB retention in early Alzheimer's disease. ACS Neuro. Chem. 5,830 (2014)).

TABLE 1 Demographic information of enrolled subjects. Group Numbers(Male/Female) Age (years) NC 6 (2/4) 53-73 DLB 9 (6/3) 65-81 AD 6 (3/3)65-87 PD 9 (5/4) 65-81 FTD 6 (0/6) 47-73 NC: normal control, DLB:dementia with Lewy Body AD: Alzheimer's disease, PD: Parkinson'sdisease, FTD: frontotemporal disease

Assay Results

The detected concentrations of Aβ₁₋₄₂, tau protein, and α-synuclein inplasma for all the subjects were shown in FIGS. 3A-3C. The detectedconcentrations of Aβ₁₋₄₂, tau protein, and α-synuclein in plasma weredenoted as φ_(Aβ1-42), φ_(tau), φ_(α-syn), respectively.

In FIG. 3A, almost all the detected concentrations of plasma Aβ₁₋₄₂ werebelow 20 pg/ml, except some data points with AD and PD. It was not easyto discriminate patients with various diseases according to theconcentration of plasma Aβ₁₋₄₂. As to the detected concentration ofplasma tau protein in FIG. 3B, NC showed relatively low concentrationsof plasma tau protein, while AD and FTD showed relatively highconcentrations. In case, it was not significant to differentiate DLBfrom PD, as well as AD from FTD. In FIG. 3C, PD could be obviouslyrecognized due to the highest level for the concentrations of plasmaα-synuclein as compared to other groups. DLB showed the second highestlevel for the concentrations of plasma α-synuclein. FTD was clearlyrecognized because of the definitely lowest level for the concentrationsof plasma α-synuclein. However, the plasma α-synuclein for NC and ADdistributed the same concentration range. It failed to discriminate NCand AD by using the concentration of plasma α-synuclein.

The results in FIGS. 3A-3C revealed the fact similar to that in FIGS. 1Aand 1B that it failed to differentiate patients with various diseases byusing single bio-marker. Multiple bio-markers were necessarily developedto achieve high discrimination among diseases.

Multiple Bio-Markers

It had been reported that the product in concentrations, denoted asφ_(Aβ1-42)×φ_(tau), of plasma Aβ₁₋₄₂ and tau protein was superior toeither of plasma Aβ₁₋₄₂ or plasma tau protein for diagnosingneurodegenerative disease, especially AD. The φ_(Aβ1-42)×φ_(tau) for allsubjects were plotted in FIG. 4. The AD and FTD patients showed highervalues for φ_(Aβ1-42)×φ_(tau) as compared to NC, DLB, and PD. With theresults in FIG. 3C, FTD patients showed the lowest level for theconcentrations of plasma α-synuclein. Thus, it was able to differentiateFTD from AD by additionally assaying plasma α-synuclein after findingφ_(Aβ1-42)×φ_(tau).

For the groups with lower values of φ_(Aβ1-42)×φ_(tau), i.e. NC, DLB,and PD, they showed different levels of φ_(α-syn), as shown in FIG. 3C.PD patients showed the highest level of φ_(α-syn), while NC subjectsshowed the lowest level of φ_(α-syn). Hence, it was able to discriminatePD, DLB, and NC by additionally assaying plasma α-synuclein afterfinding φ_(Aβ1-42)×φ_(tau). In summary, a flow chart for discriminatingsubjects of NC, DLB, AD, PD, and FTD by assaying plasma Aβ₁₋₄₂, tauprotein, and α-synuclein was proposed and shown in FIG. 5.

2D Map for Disease Discrimination

According to FIG. 5, plasma φ_(Aβ1-42)×φ_(tau) and plasma φ_(α-syn)could be used as diagnostic parameters for discriminating NC, DLB, AD,PD, and FTD. It provided a motivation to construct the two-dimensionaldistribution in the frame of plasma φ_(Aβ1-42)×φ_(tau) and plasmaφ_(α-syn), as shown in FIG. 6. In FIG. 6, the data points for variousgroups were distributed in various region. Roughly speaking, standing atthe center of the region occupied with the data points, NC wasdistributed in the lower-left region, FTD was distributed in thelower-right region, AD was roughly in the right region, PD wasdistributed in the upper region, and DLB was distributed in theupper-left region. It seemed possible to use a polar angle θ as aparameter to discriminate subjects into various disease groups, asillustrated in FIG. 7.

The polar angle θ was the angle span by a ray with respect to thehorizontal ray. The horizontal ray was not the x axis in the frame ofplasma φ_(Aβ1-42)×φ_(tau) and plasma φ_(α-syn), but started from thecenter of the region occupied with the data points. It was necessary tofind the starting point of the horizontal ray. The coordinates of thestarting point of the horizontal ray could be defined as the averagedvalues of φ_(Aβ1-42)×φ_(tau) and φ_(α-syn) of all subjects. However, thedetected values of φ_(Aβ1-42)×φ_(tau) or φ_(α-syn) distributed overseveral orders of magnitude. Points with higher values would be moreweighted when calculating the average value of all points. This was thereason why FIG. 6 or FIG. 7 was not plotted in the linear-to-linearscale. Instead, FIG. 6 and FIG. 7 were plotted in the log-to-log scale.

The detected values of all points in FIG. 6 were transferred vialogarithm. The log(φ_(α-syn)) versus log(φ_(Aβ1-42)×φ_(tau)) wereplotted in FIG. 8. Hereafter, the values of log(φ_(α-syn)) andlog(φ_(Aβ1-42)×φ_(tau)) were referred as to original concentrations. Itwas found that the values of all log(φ_(α-syn))'s or alllog(φ_(Aβ1-42)×φ_(tau))'s were distributed at the same order ofmagnitude. For example, log(φ_(α-syn))'s were within the range from −6to 2, and log(φ_(Aβ1-42)×φ_(tau))'s were within the range from 1.6 to3.6. Now, each data point was equally weighted when calculating theiraveraged values of log(φ_(α-syn))'s and log(φ_(Aβ1-42)×φ_(tau))'s. Inaddition, the standard deviations of all log(φ_(α-syn))'s and alllog(φ_(Aβ1-42)×φ_(tau))'s were calculated. Then, each log(φ_(α-syn)) andlog(φ_(Aβ1-42)×φ_(tau)) were transferred via the following equations:

φ′_(Aβ1-42×tau)=[log(φ_(Aβ1-42)×φ_(tau))−M_(log()φ_(Aβ1-42)×φ_(tau))]/SD_(log()φ_(Aβ1-42)×φ_(tau)),   (Eq. 1)

φ′_(α-syn)=[log(φ_(α-syn))−M _(log()φ_(α-syn))]/SD_(log()φ_(α-syn)),  (Eq. 2)

Where M_(log()φ_(Aβ1-42)×φ_(tau)) and SD_(log()φ_(Aβ1-42)×φ_(tau))denoted the averaged value and standard deviation of alllog(φ_(Aβ1-42)×φ_(tau))'s, M_(log()φ_(α-syn)) and SD_(log()φ_(α-syn))denoted the averaged value and standard deviation of alllog(φ_(α-syn))'s. The φ′_(Aβ1-42×tau) and φ′_(α-syn), which werereferred as to modulated concentrations, were plotted in FIG. 9.

The origin in the frame of φ′_(α-syn) and φ′_(Aβ1-42×tau) was thestarting point of the horizontal ray in FIG. 7. That was, the horizontalray was the x axis of FIG. 9.

Polar Angle for Disease Discrimination

In FIG. 9, there existed a boundary which optimally separated subjectsin two disease groups locating in neighboring regions. The boundarycould be determined by suitably constructing a ray along a certain polarangle θ′ from the origin in the frame of φ′_(α-syn) and φ′_(Aβ1-42×tau).An example to construct boundary optimally separating NC and DLB wasgiven. Other boundaries for optimally separating two neighboring groupsin FIG. 9 can be constructed by following the same processes.

Firstly, each point of NC group and DLB group was assigned with a polarangle θ′. For a given point i with the coordinate (φ′_(Aβ1-42×tau,i),φ′_(α-syn,i)) in FIG. 9, the polar angle θ′_(i) was obtained via

θ′_(i)=tan⁻¹(φ′_(α-syn,i)/φ′_(Aβ1-42×tau,i))

Among the points in NC and DLB groups, there existed a minimum polarangle, referred as θ′_(min). Every θ′_(i) was subtracted with θ′_(min)to get the shifted polar angle θ′_(s,i), i.e.

θ′_(s,i)=θ′_(i)−θ′_(min)

The θ′_(s)'s for points belonging to NC and DLB groups in FIG. 9 wereplotted in FIG. 10. Through the analysis of receiver operatingcharacteristic (ROC) curve, the cut-off value of θ′_(s) to optimallydiscriminate NC and DLB subjects was found to be 225.28°, as plottedwith a dashed line in FIG. 10. The corresponding sensitivity andspecificity were 0.833 and 1.000. By adding θ′_(min) to 225.28°, thepolar angle optimally discriminating NC and DLB groups in FIG. 9 was189.48°. The ray along the polar angle 189.48° was plotted with thesolid line in FIG. 11.

The boundaries optimally separating neighboring groups in FIG. 9 couldbe found, as plotted with solid lines in FIG. 12.

Utilization of 2D Map for Disease Diagnosis

With the boundaries in FIG. 12, the two-dimensional map in the frame ofφ′_(α-syn) and φ′_(Aβ1-42×tau) were divided into several quadrants. Eachquadrant corresponded to one kind of diseases. Once the concentrationsof plasma Aβ₁₋₄₂, tau protein, and α-synuclein of a subject had beendetected, the modulated concentrations could be obtained via Eqs. (1)and (2). Then, the position of modulated concentrations with thissubject could be found in FIG. 12. The subject could be accuratelydiagnosed.

One skilled in the art readily appreciates that the present invention iswell adapted to carry out the objects and obtain the ends and advantagesmentioned, as well as those inherent therein. The biomarkers and usesthereof are representative of preferred embodiments, are exemplary, andare not intended as limitations on the scope of the invention.Modifications therein and other uses will occur to those skilled in theart. These modifications are encompassed within the spirit of theinvention and are defined by the scope of the claims.

It will be readily apparent to a person skilled in the art that varyingsubstitutions and modifications may be made to the invention disclosedherein without departing from the scope and spirit of the invention.

All patents and publications mentioned in the specification areindicative of the levels of those of ordinary skill in the art to whichthe invention pertains. All patents and publications are hereinincorporated by reference to the same extent as if each individualpublication was specifically and individually indicated to beincorporated by reference.

The invention illustratively described herein suitably may be practicedin the absence of any element or elements, limitation or limitations,which are not specifically disclosed herein. The terms and expressionswhich have been employed are used as terms of description and not oflimitation, and there is no intention that in the use of such terms andexpressions of excluding any equivalents of the features shown anddescribed or portions thereof, but it is recognized that variousmodifications are possible within the scope of the invention claimed.Thus, it should be understood that although the present invention hasbeen specifically disclosed by preferred embodiments and optionalfeatures, modification and variation of the concepts herein disclosedmay be resorted to by those skilled in the art, and that suchmodifications and variations are considered to be within the scope ofthis invention as defined by the appended claims.

What is claimed is:
 1. A method for constructing quadrants correspondingto different diseases in a frame of concentrations of multipleindependent biomarkers, comprising: (a) transferring originaldistributed concentrations of every independent biomarker to modifieddistributed concentrations, comprising: calculating the mean value andthe standard deviation of the original distributed concentrations for agiven independent biomarker; individually subtracting all the originaldistributed concentrations by the mean value for the given independentbiomarker; and individually dividing all the differences by the standarddeviation to get the modified distributed concentrations for the givenindependent biomarker; (b) positing the modified distributedconcentrations in a frame of multiple independent biomarkers; and (c)finding a boundary optimally separating neighboring quadrantscorresponding to different diseases.
 2. The method of claim 1, whereinthe original distributed concentrations are originally detectedconcentrations or transferred concentrations of the originally detectedconcentrations via mathematic calculation.
 3. The method of claim 2,wherein the mathematic calculation is logarithm, trigonometric function,sigmoid function, or any combinations thereof.
 4. The method of claim 1,wherein the independent biomarkers are selected from the groupconsisting of a single kind of bio-molecule and a combination of severalkinds of bio-molecules.
 5. The method of claim 1, wherein theindependent biomarkers exist in blood, urine, cerebrospinal fluid, orsaliva.
 6. The method of claim 1, wherein the number of the multipleindependent biomarkers is more than one.
 7. The method of claim 1,wherein the method for finding a boundary optimally separatingneighboring quadrants corresponding to different diseases in step (c) isROC curve analysis.
 8. The method of claim 1, wherein the independentbiomarkers are plasma α-synuclein, β-amyloid, tau protein, and theirderivatives to construct quadrants corresponding to healthy subjects andpatients with neurodegenerative disease.
 9. The method of claim 8,wherein the neurodegenerative disease is dementia with Lewy body,Parkinson's disease, Alzheimer's disease, or frontotemporal dementia.